Improving the Gaussianity of Radar Reflectivity Departures between Observations and Simulations by Using the Symmetric Rain Rate

Abstract. Given that the Gaussianity of observation error distribution is the fundamental principle of some data assimilation and machine learning algorithms, the error structure of radar reflectivity becomes increasingly important with the development of high resolution forecasts and nowcasts of convective systems. This study examines the error distribution of radar reflectivity and discusses what give rise to the non-Gaussian error distribution by using 6 month observations minus backgrounds (OmBs) of composites of vertical maximum reflectivity (CVMRs) in mountainous and hilly areas. By following the symmetric error model in all-sky satellite radiance assimilation, we unveil the error structure of CVMRs as a function of symmetric rain rates, which is the average of observed and simulated rain rates. Unlike satellite radiance, the error structure of CVMRs shows a sharper slope in light precipitations than moderate precipitations. Thus, a three-piecewise fitting function is more suitable for CVMRs. The probability density functions of OmBs normalized by symmetric rain rates become more Gaussian in comparison with the probability density function normalized by the whole samples. Moreover, the possibility of using third-party predictor to construct the symmetric error model are also discussed in this study. The Gaussianity of OmBs can be further improved by using a more accurate precipitation observations. According to the Jensen-Shannon divergence, a more linear predictor, the logarithmic transformation of rain rate, can provide the most Gaussian error distribution in comparison with other predictors.